Strictly semi-transitive operator algebras
| dc.creator | Rosenthal, H. P. | |
| dc.creator | Troitsky, V. G. | |
| dc.date | 2003-09-01 | |
| dc.date.accessioned | 2026-07-07T05:00:43Z | |
| dc.date.available | 2026-07-07T05:00:43Z | |
| dc.description | An algebra A of operators on a Banach space X is called strictly semi-transitive if for all non-zero x,y in X there exists an operator S in A such that Sx=y or Sy=x. We show that if A is norm-closed and strictly semi-transitive, then every A-invariant linear subspace is norm-closed. Moreover, Lat A is totally and well ordered by reverse inclusion. If X is complex and A is transitive and strictly semi-transitive, then A is WOT-dense in L(X). It is also shown that if A is an operator algebra on a complex Banach space with no invariant operator ranges, then A is WOT-dense in L(X). This generalizes a similar result for Hilbert spaces proved by Foias. | |
| dc.description | To appear in Journal of Operator Theory | |
| dc.identifier | https://arxiv.org/abs/math/0309014 | |
| dc.identifier | http://arxiv.org/abs/math/0309014 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68428 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 47A15; 47L10 | |
| dc.title | Strictly semi-transitive operator algebras | |
| dc.type | text |